We study fairness in decision-making when the data may encode systematic bias. Existing approaches typically impose fairness constraints while predicting the observed decision, which may itself be unfair. We propose a novel framework for characterising and addressing fairness issues by introducing the notion of desert decision, a latent variable representing the decision an individual rightfully deserves based on their actions, efforts, or abilities. This formulation shifts the prediction target from the potentially biased observed decision to the desert decision. We advocate achieving fair decision-making by predicting the desert decision and assessing unfairness by the discrepancy between desert and observed decisions. We establish nonparametric identification results under causally interpretable assumptions on the fairness of the desert decision and the unfairness mechanism of the observed decision. For estimation, we develop a sieve maximum likelihood estimator for the desert decision rule and an influence-function-based estimator for the degree of unfairness. Sensitivity analysis procedures are further proposed to assess robustness to violations of identifying assumptions. Our framework connects fairness with measurement error models, aligning predictive accuracy with fairness relative to an appropriate target, and providing a structural approach to modelling the unfairness mechanism.

翻译：我们研究在数据可能编码系统性偏差时决策中的公平性问题。现有方法通常在对观测到的决策进行预测时施加公平性约束，而该决策本身可能就是不公平的。我们提出一种新框架来描述和解决公平性问题，通过引入"沙漠决策"这一概念——基于个体行为、努力或能力而应得的潜在决策变量。该公式将预测目标从可能带有偏差的观测决策转向沙漠决策。我们主张通过预测沙漠决策来实现公平决策，并通过沙漠决策与观测决策之间的差异来评估不公平性。我们在沙漠决策的公平性和观测决策的不公平机制的可因果解释假设下，建立了非参数识别结果。在估计方面，我们发展了沙漠决策规则的筛极大似然估计器，以及用于量化不公平程度的影响函数估计器。进一步提出敏感性分析程序以评估对识别假设违反的稳健性。我们的框架将公平性与测量误差模型联系起来，使预测准确性与针对适当目标的公平性保持一致，并提供了一种建模不公平机制的结构化方法。